Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅1018

@article{Silva2014EmpiricalVO,
title={Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅1018},
author={Tom{\'a}s Oliveira e Silva and Siegfried Herzog and Silvio Pardi},
journal={Math. Comput.},
year={2014},
volume={83},
pages={2033-2060}
}
• Published 18 November 2013
• Computer Science, Mathematics
• Math. Comput.
This paper describes how the even Goldbach conjecture was confirmed to be true for all even numbers not larger than 4 · 1018. Using a result of Ramaré and Saouter, it follows that the odd Goldbach conjecture is true up to 8.37 · 1026. The empirical data collected during this extensive verification effort, namely, counts and first occurrences of so-called minimal Goldbach partitions with a given smallest prime and of gaps between consecutive primes with a given even gap, are used to test several… Expand

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